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Given a mixture of: a saturated solution of a solute in a solvent together with excess of the solute compound as crystalline material.

If one were to change the bulk composition of the mixture by removing some of the solution could this cause dissolution or precipitation of the solid in the remaining mixture, or the concentration of the remaining solution?

Presumably one should expect some crystallisation in the portion of the solution that is removed from the mixture?

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If one were to change the bulk composition of the mixture by removing some of the solution [...]

This does not change the composition of the solution above the solid. Since the concentration of the solute remains constant, I do not expect a change.

Presumably one should expect some crystallisation in the portion of the solution that is removed from the mixture?

It still is a saturated solution. Unless you evaporate the solvent (= increase the concentration of the solute) or change the temperature, nothing will change.

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When a solution is saturated, the remaining solid is in equilibrium with the solvent: $$\ce{AB<=>[solv.]A+_{(solv)} + B-_{(solv)}}$$

That means that there is as much of your solid solved. If you take out some of the solution then the concentration remains the same, in your original flask as well as in the portion you withdraw.

If you remove only solvent, i.e. by heating your solution or diffusion over time. In this withdrawn portion crystals will form. The concentration will not change, only the amount of substance $n$ in your solution will change as the volume shrinks ($c=\frac{n}{V}$).

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